In present work an effective method to research geometrically nonlinear free vibrations of elements of thinwalled
constructions that can be modeled as laminated shallow shells with complex planform is applied. The
proposed method is based on joint use of R-functions theory, variational methods and Bubnov-Galerkin
procedure. It allows reducing an initial nonlinear system of motion equations of a shallow shell to the Cauchy
problem. The mathematical formulation of the problem is performed in a framework of the refined first-order
theory. The appropriate software is created within POLE-RL program system for polynomial results and using
C+ + programs for splines. New problems of linear and nonlinear vibrations of laminated shallow shells with
cutouts are solved. To confirm reliability of the obtained results their comparison with the ones obtained using
spline-approximation and known in literature is provided. Effect o f boundary condition on cutout is studied.
